Probability and Statistics in Hydrology treats probability theory and mathematical statistics as applied to hydrology. Probability theory is presented in a summarized form with emphasis on its use in hydrology. Statistically, the emphasis is on inferential rather than descriptive statistics of classical hydrologic applications.

Since hydrologic processes in nature are governed by the laws of chance, the use of probability theory and mathematical statistics is unavoidable in the extraction of information from hydrologic data and for the best mathematical description of these processes. This book is not a conventional statistical treatment of the subject. Certain concepts are defined; mathematical expressions are written in a format that is ready to use; techniques are explained, as well as their applications to hydrology (with examples) are presented. This book is aimed at practicing hydrologists and engineers; graduate students; post-graduate students; and specialist interested in probability theory and mathematical statistics as applied to hydrology. It is now part of WRP’s Classic Resource Edition.

3 VARIOUS PROBABILITY TOPICS APPLIED TO HYDROLOGY
Combinatorial Analysis
Geometric Probabilities
Applications of the Theorem of Total Probability and the Bayes's Theorem
Limit Theorems
Markov Chains
Mathematical Expectation, and Variance of Random Variables . .
Law of Large Numbers
Problems for Discussion and Solutions

4 STATISTICS AND HYDROLOGY
Relationship of Statistics to Probability Theory
Statistics as Description Numbers
Mathematical Statistical Models
Concepts of Risk and Uncertainty in Hydrology
Statistics in Hydrology
Problems for Discussion and Solutions

6 PARAMETERS AND ORDER-STATISTICS AS DESCRIPTORS OF DISTRIBUTIONS
Parameters and Order-Statistics
Descriptors of Central Tendency
Descriptors of Dispersion
Descriptors of Asymmetry
Descriptors of Flatness
Application Areas of Descriptors of Univariate Distributions
in Hydrology and Water Resources
6.7 Descriptors of Distributions of Bivariates, Multivariates,
and Conditional Variables
6.8 Problems for Discussion and Solutions

9 SAMPLING THEORY
Basic Definitions and Approaches
Parameters of Distributions of Basic Statistics
Sampling Distribution Functions
Confidence and Tolerance Intervals and Limits
Content of Information in Various Parameters
Problems for Discussion and Solutions

10 TESTING HYPOTHESES AND GOODNESS OF FIT
Definitions of Hypotheses and Their Testing
Testing Simple and Composite Hypotheses
Testing the Goodness of Fit of Probability Functions to Empirical Distributions
Problems for Discussion and Solutions